Please post that other photo you have. That one shows the sloped ceiling more clearly.

As requested by homebound, I am attaching the other photograph.

Well, you could move the cased door opening into the room (toward the viewer in the first picture) so it is flush with the sloped wall. That would eliminate the flat section of ceiling (with the recessed light) and would give you two flat walls intersecting. But that would be a costly change at this point (I would think) and you'd still be dealing with a fairly contemporary room that you're trying to "traditionalize" with crown molding. Your arched opening doesn't have much room for molding (is there 5-1/4" there?), and I don't know that a vaulted ceiling with a skylight easily lends itself to crown moldings.

What if you were to flip the idea on its head and go with some sort of wainscoting? You'd eliminate the ceiling problem, but would still have a more traditional treatment for the room.

Drop the ceiling in that alcove or put just enough of a header in the opening to run the molding.

What pal said: either lower the ceiling in the hall/alcove or drywall in a "beam" of sorts at that opening. Either method gives you more "face" on the DR wall for the crown on the sloping ceiling to meet the adjoining wall.

Thank you everyone for your thoughts. I spoke with our finish carpenter yesterday about the ideas you proposed, and today he implemented the idea of putting a beam (actually a 2 x 4) across the opening, added crown in the small ceiling area between this opening and the door opening (leading to the bedroom wing). Then on the dining room side of the opening, he then proceeded to extend the crown molding down the sloping ceiling. He finished off by trimming the underside of this 2 x 4 and it looks great!

Thank you again!

Can you post an after photo?

Yes please post a picture! I too have rake ceilings that intersect with flat and would love to have crown molding, but could never imagine it working. More photos please! Thanks.

As requested, I'm posting a couple of pictures. It will be in a couple of different posts, since I have not yet been able to figure out out to post more than one picture per post. This is a picture of the "after" from the same frontal perspective as the before.

The carpenter was debating whether to box it with something larger (with a 4 x 4) but ultimately decided against that. He said that if he used a 4 x 4 as the "header", he felt like he would have to case out this opening, which would look a little awkward for what this opening is (or isn't).

Another photo, as viewed from the bedroom hallway side and underneath.

That is a good solution.

looks nice!